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It is also related with another particularity of order statistics of uniform random variables: It follows from the BRS-inequality that the maximum expected number of uniform U(0,1] random variables one can choose from a sample of size n with a sum up not exceeding < < / is bounded above by , which is thus invariant on the set of all , with ...
The zeta distribution has uses in applied statistics and statistical mechanics, and perhaps may be of interest to number theorists. It is the Zipf distribution for an infinite number of elements. The Hardy distribution , which describes the probabilities of the hole scores for a given golf player.
Related changes; Upload file; Special pages; Permanent link; ... In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant. [1] [2] References
For any population probability distribution on finitely many values, and generally for any probability distribution with a mean and variance, it is the case that +, where Q(p) is the value of the p-quantile for 0 < p < 1 (or equivalently is the k-th q-quantile for p = k/q), where μ is the distribution's arithmetic mean, and where σ is the ...
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
In the case where the range of values is countably infinite, these values have to decline to zero fast enough for the probabilities to add up to 1. For example, if p ( n ) = 1 2 n {\displaystyle p(n)={\tfrac {1}{2^{n}}}} for n = 1 , 2 , . . . {\displaystyle n=1,2,...} , the sum of probabilities would be 1 / 2 + 1 / 4 + 1 / 8 + ⋯ = 1 ...
K-distribution arises as the consequence of a statistical or probabilistic model used in synthetic-aperture radar (SAR) imagery. The K-distribution is formed by compounding two separate probability distributions, one representing the radar cross-section, and the other representing speckle that is a characteristic of coherent imaging. It is also ...
Consider, as an example, the k-nearest neighbour smoother, which is the average of the k nearest measured values to the given point. Then, at each of the n measured points, the weight of the original value on the linear combination that makes up the predicted value is just 1/k. Thus, the trace of the hat matrix is n/k.